Problem: A man spent two-thirds of his money and misplaced one-third of the remainder, leaving him with $\$22$. How much money did he originally have?
Explanation: Let $x$ be the amount of money he originally had. After spending two-thirds of his money, he is left with $\frac{1}{3}x$. After losing one-third of that, he is left with $\frac{2}{3}\cdot\frac{1}{3}x = \frac{2}{9}x = 22$ dollars. Solving for $x$, we see that $x = \boxed{99}$.